Design weights are used to compensate for non-proportional stratification. For example, in a population containing 100,000,000 men and 100,000,000 women, if you used quotas or stratification to achieve a sample of 80 men and 20 women, then a design weight is created to take this non-proportional stratification into account.
The probability of selecting men in this sample is 80 / 100,000,000 = 0.0000008 and the probability for women is 0.0000002. So, each man in the sample is assigned a weight of 1,250,000 and each woman a weight of 5,000,000.
In jargon: design weights are computed as the inverse of the selection probability (D. G. Horvitz and D. J. Thompson (1952), “A Generalization of Sampling Without Replacement From a Finite Universe”, Journal of the American Statistical Association, Vol. 47, No. 260 (Dec., 1952), pp. 663-685.)
Typically, these weights are then further adjusted to take an average value of 1.0 (i.e., the raw values are divided by their average).
Approaches to dealing with design weights include:
- Computing a design weight as described here and using it in analysis.
- Including the stratification variable as an adjustment variable when creating Rim weights/Raking or Calibration.